Previous literature has shown that the introduction of homogeneous perforation on plates and cylinders decreases aerodynamic drag. Here, it is shown that the opposite is true for a sphere; drag can increase with porosity. Hollow porous spheres exposed to a uniform free stream are studied experimentally using force and flow field measurements. The parameter space encompasses moderate to high Reynolds numbers ($5 \times 10^4 \leq \textit{Re} \leq 4 \times 10^5$) and porosities ranging from $0\,\%$ to $80\,\%$. The main conclusion is that drag increases with porosity, at super-critical Reynolds numbers, for all studied porosities. At low porosities (less than $9\,\%$), the effect of porosity on drag can be explained by shifts in the separation point. At higher porosities the drag increase cannot be explained by separation shifts, and instead is explained by two competing forms of kinetic energy dissipation: (i) shear on the macro-scale of the body, and (ii) hole losses from flow through the pores. The former generally decreases with porosity, as bleeding flow passing through the body decreases the characteristic velocity difference in the body-scale wake. In a sphere, hole losses increase with porosity sufficiently fast to overcome decreasing body-scale shear losses, in contrast to plates and cylinders where this is not the case. Relatively weak wake vortex structures, and associated low drag coefficient at zero porosity, for a sphere reduce the impact of wake bleeding. Moreover, fluid entering the fore of a sphere can exit perpendicular to the free stream, further reducing wake bleeding while still contributing to hole losses.

This work aims to complement the description of the atomisation process in a typical commercial pressure-swirl atomiser. Conventional characterisation focuses on the final spray, where established experimental techniques allow for measuring spherical droplets in a dilute regime. However, the early stages of atomisation involve distorted liquid structures with complex interface morphology that challenge both experimental and numerical approaches. While numerical simulations with interface-capturing methods have provided access to this region, they currently remain computationally prohibitive to follow the atomisation process until the formation of the final spherical droplets. To characterise the evolving interface morphology, we propose analysing the curvature distribution obtained from both simulations and two-photon laser-induced fluorescence (2P-LIF) imaging. This curvature-based methodology, recently developed to characterise numerical sprays (Palanti et al. Intl J. Multiphase Flow 147, 2022, 103879; Ferrando et al. Atomiz. Sprays 33, 2023, 1–28), is here extended to experimental data. Both approaches are compared with available phase Doppler anemometry (PDA) measurements performed further downstream on spherical droplets. The morphological evolution of the atomising spray is interpreted through curvature statistics, which provide a unified framework applicable to all atomisation stages. When applied to spherical droplets, the curvature distribution recovers the conventional drop size distribution, linking early interface deformation to the final spray structure. The birth of this final drop size distribution can thus be observed by comparing the three approaches – numerical simulation limited to the early stage of atomisation, curvature derived from 2P-LIF images limited to two-dimensional (2-D) contour analysis, and PDA measurements of the dilute spray. The results show that curvature properties evolve in a way that can be directly representative of the final spray even at early atomisation stages.

A lattice Boltzmann method is adopted to investigate the breakup of surfactant-free and surfactant-laden droplets in both regular and irregular T-junction microchannels. During droplet neck contraction, the neck thinning shifts from inertia dominated to interfacial tension dominated, causing spontaneous rapid neck collapse due to Rayleigh–Plateau instability. For the regular rectangular microchannels, we find that the prerequisite for the spontaneous breakup of a surfactant-free droplet is that the local capillary pressure in the triggering area exceeds the Laplace pressure difference between the inside and outside of the droplet neck. Results show that the critical neck thickness $\delta _\textit{cr}^{*}$ for the droplet spontaneous breakup increases with increasing height-to-width ratio $\chi$ of the microchannel in both surfactant-free and surfactant-laden systems. The presence of surfactants decreases $\delta _\textit{cr}^{*}$ at the identified $\chi$, while the surfactant effects are gradually enhanced as $\chi$ increases. Subsequently, a constriction section is incorporated into the upper microchannel wall to establish an irregular microchannel. As constriction depth (length) increases, $\delta _\textit{cr}^{*}$ linearly decreases (increases) in the surfactant-free system, while $\delta _\textit{cr}^{*}$ exponentially decreases (linearly increases) in the surfactant-laden system. Four empirical formulas are proposed to predict the values of $\delta _\textit{cr}^{*}$ under varying constriction depths and lengths in the two systems.

The effects of confinement and polydispersity on the shear-induced diffusivity of non-Brownian, neutrally buoyant spheres suspended in a Newtonian fluid are investigated using simulations that incorporate short-range lubrication forces, surface roughness and frictional contacts. Simulations were performed at a fixed volume fraction of 0.45 for multiple values of particle roughness and friction coefficient. Confinement by bounding walls promoted layered structures that suppressed particle mobility and reduced diffusivity, while also diminishing the influence of friction and roughness. In contrast, high polydispersity disrupted layering and enhanced diffusivity, even in confined systems. Polydispersity also led to size-dependent demixing, with smaller particles preferentially migrating towards the walls and exhibiting higher mobility. These results have implications for modelling and controlling transport in suspensions, where confinement and polydispersity alter the effects of friction and roughness on shear-induced diffusion.

The classical problem of steady rarefied gas flow past an infinitely thin circular disk is revisited, with particular emphasis on the gas behaviour near the disk edge. The uniform flow is assumed to be perpendicular to the disk surface. An integral equation for the velocity distribution function, derived from the linearised Bhatnagar–Gross–Krook model of the Boltzmann equation and subject to diffuse reflection boundary conditions, is solved numerically. The numerical method fully accounts for the discontinuity in the velocity distribution function that arises due to the presence of the edge. It is found that a kinetic boundary layer forms near the disk edge, extending over several mean free paths, and that its magnitude scales as $\textit{Kn}^{1/2}$ as the Knudsen number $\textit{Kn}$ (defined with respect to the disk radius) tends to zero. A thermal polarisation effect, previously studied for spherical geometries, is also observed in the disk case, with a more pronounced manifestation near the edge that exhibits the same $\textit{Kn}^{1/2}$ scaling. The drag force acting on the disk is computed over a wide range of Knudsen numbers and shows good agreement with existing results for a hard-sphere gas and in the near-free-molecular regime.

In Navier–Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional (3-D) NS equations indicate that employing observational data resolved down to a specific length scale, $\ell ^{\rm 3\text{-}D}_{\ast }$, enables the successful reconstruction of small-scale flows. Such a length scale of ‘essential resolution of observation’ for reconstruction $\ell ^{\rm 3\text{-}D}_{\ast }$ is close to the dissipation scale in three-dimensional NS turbulence. Here, we study the equivalent length scale in two-dimensional (2-D) NS turbulence, $\ell ^{\rm 2\text{-}D}_{\ast }$, and compare with the three-dimensional case. Our numerical studies using data assimilation and conditional Lyapunov exponents reveal that, for Kolmogorov flows with Ekman drag, the length scale $\ell ^{\rm 2\text{-}D}_{\ast }$ is actually close to the forcing scale, substantially larger than the dissipation scale. Furthermore, we discuss the origin of the significant relative difference between the length scales, $\ell ^{\rm 2\text{-}D}_{\ast }$ and $\ell ^{\rm 3\text{-}D}_{\ast }$, based on inter-scale interactions, ‘cascades’ and orbital instabilities in turbulence dynamics.